OpenRaiser/Intern-Atlas huggingface dataset:
Properties of an Aloha-like stability region
Venue: arXiv cs.IT 2017
Year: 2017

A well-known inner bound on the stability region of the finite-user slotted Aloha protocol is the set of all arrival rates for which there exists some choice of the contention probabilities such that the associated worst-case service rate for each user exceeds the user's arrival rate, denoted $Λ$. Although testing membership in $Λ$ of a given arrival rate can be posed as a convex program, it is nonetheless of interest to understand the properties of this set. In this paper we develop new results of this nature, including $i)$ an equivalence between membership in $Λ$ and the existence of a positive root of a given polynomial, $ii)$ a method to construct a vector of contention probabilities to stabilize any stabilizable arrival rate vector, $iii)$ the volume of $Λ$, $iv)$ explicit polyhedral, spherical, and ellipsoid inner and outer bounds on $Λ$, and $v)$ characterization of the generalized convexity properties of a natural ``excess rate'' function associated with $Λ$, including the convexity of the set of contention probabilities that stabilize a given arrival rate vector.
A New Non-MDS Hash Function Resisting Birthday Attack and Meet-in-the-middle Attack
Venue: arXiv cs.CR 2017
Year: 2017

To examine the integrity and authenticity of an IP address efficiently and economically, this paper proposes a new non-Merkle-Damgard structural (non-MDS) hash function called JUNA that is based on a multivariate permutation problem and an anomalous subset product problem to which no subexponential time solutions are found so far. JUNA includes an initialization algorithm and a compression algorithm, and converts a short message of n bits which is regarded as only one block into a digest of m bits, where 80 <= m <= 232 and 80 <= m <= n <= 4096. The analysis and proof show that the new hash is one-way, weakly collision-free, and strongly collision-free, and its security against existent attacks such as birthday attack and meet-in-the- middle attack is to O(2 ^ m). Moreover, a detailed proof that the new hash function is resistant to the birthday attack is given. Compared with the Chaum-Heijst-Pfitzmann hash based on a discrete logarithm problem, the new hash is lightweight, and thus it opens a door to convenience for utilization of lightweight digital signing schemes.
The Corruption Bound, Log Rank, and Communication Complexity
Venue: arXiv cs.CC 2017
Year: 2017

We prove upper bounds on deterministic communication complexity in terms of log of the rank and simple versions of the corruption bound. Our bounds are a simplified version of the results of Gavinsky and Lovett, using the same set of tools. We also give an elementary proof for the upper bound on communication complexity in terms of rank proved by Lovett.
Speculate-Correct Error Bounds for k-Nearest Neighbor Classifiers
Venue: arXiv cs.LG 2017
Year: 2017

We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(sqrt((k + ln n) / n)) error bound range for n in-sample examples.
A Regularization Approach to Blind Deblurring and Denoising of QR Barcodes
Venue: arXiv cs.CV 2017
Year: 2017

QR bar codes are prototypical images for which part of the image is a priori known (required patterns). Open source bar code readers, such as ZBar, are readily available. We exploit both these facts to provide and assess purely regularization-based methods for blind deblurring of QR bar codes in the presence of noise.
Only distances are required to reconstruct submanifolds
Venue: arXiv cs.CG 2017
Year: 2017

In this paper, we give the first algorithm that outputs a faithful reconstruction of a submanifold of Euclidean space without maintaining or even constructing complicated data structures such as Voronoi diagrams or Delaunay complexes. Our algorithm uses the witness complex and relies on the stability of power protection, a notion introduced in this paper. The complexity of the algorithm depends exponentially on the intrinsic dimension of the manifold, rather than the dimension of ambient space, and linearly on the dimension of the ambient space. Another interesting feature of this work is that no explicit coordinates of the points in the point sample is needed. The algorithm only needs the distance matrix as input, i.e., only distance between points in the point sample as input.
Verifying Chemical Reaction Network Implementations: A Pathway Decomposition Approach
Venue: arXiv cs.CE 2017
Year: 2017

Here we focus on the challenge of verifying the correctness of molecular implementations of abstract chemical reaction networks, where operation in a well-mixed "soup" of molecules is stochastic, asynchronous, concurrent, and often involves multiple intermediate steps in the implementation, parallel pathways, and side reactions. This problem relates to the verification of Petri nets, but existing approaches are not sufficient for providing a single guarantee covering an infinite set of possible initial states (molecule counts) and an infinite state space potentially explored by the system given any initial state. We address these issues by formulating a new theory of pathway decomposition that provides an elegant formal basis for comparing chemical reaction network implementations, and we present an algorithm that computes this basis. Our theory naturally handles certain situations that commonly arise in molecular implementations, such as what we call "delayed choice," that are not easily accommodated by other approaches. We further show how pathway decomposition can be combined with weak bisimulation to handle a wider class that includes most currently known enzyme-free DNA implementation techniques. We anticipate that our notion of logical equivalence between chemical reaction network implementations will be valuable for other molecular implementations such as biochemical enzyme systems, and perhaps even more broadly in concurrency theory.
The Kolmogorov-Zakharov Model for Optical Fiber Communication
Venue: arXiv cs.IT 2017
Year: 2017

A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourier modes and studying the role of the resonant, non-resonant, and trivial quartets in the dynamics. As an application, a power spectral density is suggested for calculating the interference power in dense wavelength-division multiplexed optical systems, based on the kinetic equation of the WWT. This power spectrum, termed the Kolmogorov-Zakharov (KZ) model, results in a better estimate of the signal spectrum in optical fiber, compared with the so-called Gaussian noise (GN) model. The KZ model is generalized to non-stationary inputs and multi-span optical systems.
Completion of the mixed unit interval graphs hierarchy
Venue: arXiv cs.DM 2017
Year: 2017

We describe the missing class of the hierarchy of mixed unit interval graphs, generated by the intersection graphs of closed, open and one type of half-open intervals of the real line. This class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as quadratic-time algorithms that recognize graphs from this class and produce a corresponding interval representation if one exists. We also mention that the work in arXiv:1405.4247 directly extends to provide a quadratic-time algorithm to recognize the class of mixed unit interval graphs.
On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism
Venue: arXiv cs.DS 2017
Year: 2017

In the Maximum Common Induced Subgraph problem (henceforth MCIS), given two graphs $G_1$ and $G_2$, one looks for a graph with the maximum number of vertices being both an induced subgraph of $G_1$ and $G_2$. MCIS is among the most studied classical NP-hard problems. It remains NP-hard on many graph classes including forests. In this paper, we study the parameterized complexity of MCIS. As a generalization of \textsc{Clique}, it is W[1]-hard parameterized by the size of the solution. Being NP-hard even on forests, most structural parameterizations are intractable. One has to go as far as parameterizing by the size of the minimum vertex cover to get some tractability. Indeed, when parameterized by $k := \text{vc}(G_1)+\text{vc}(G_2)$ the sum of the vertex cover number of the two input graphs, the problem was shown to be fixed-parameter tractable, with an algorithm running in time $2^{O(k \log k)}$. We complement this result by showing that, unless the ETH fails, it cannot be solved in time $2^{o(k \log k)}$. This kind of tight lower bound has been shown for a few problems and parameters but, to the best of our knowledge, not for the vertex cover number. We also show that MCIS does not have a polynomial kernel when parameterized by $k$, unless $NP \subseteq \mathsf{coNP}/poly$. Finally, we study MCIS and its connected variant MCCIS on some special graph classes and with respect to other structural parameters.
Scheduling with two non-unit task lengths is NP-complete
Venue: arXiv cs.CC 2017
Year: 2017

The non-preemptive job scheduling problem with release times and deadlines on a single machine is fundamental to many scheduling problems. We parameterize this problem by the set of job lengths the jobs can have. The case where all job lengths are identical is known to be solvable in polynomial time. We prove that the problem with two job lengths is NP-complete, except for the case in which the short jobs have unit job length, which was already known to be efficiently solvable. The proof uses a reduction from satisfiability to an auxiliary scheduling problem that includes a set of paired jobs that each have both an early and a late deadline, and of which at least one should be scheduled before the early deadline. This reduction is enabled by not only these pairwise dependencies between jobs, but also by dependencies introduced by specifically constructed sets of jobs which have deadlines close to each other. The auxiliary scheduling problem in its turn can be reduced to the scheduling problem with two job lengths by representing each pair of jobs with two deadlines by four different jobs.
Complexity issues in some clustering problems in combinatorial circuits
Venue: arXiv cs.DS 2017
Year: 2017

The modern integrated circuit is one of the most complex products that has been engineered to-date. It continues to grow in complexity as the years progress. As a result, very large-scale integrated (VLSI) circuit design now involves massive design teams employing state-of-the art computer-aided design (CAD) tools. One of the oldest, yet most important CAD problems for VLSI circuits is physical design automation, where one needs to compute the best physical layout of millions to billions of circuit components on a tiny silicon surface \cite{Lim08}. The process of mapping an electronic design to a chip involves a number of physical design stages, one of which is clustering. In this paper, we focus on problems in clustering which are critical for more sustainable chips. The clustering problem in combinatorial circuits alone is a source of multiple models. In particular, we consider the problem of clustering combinatorial circuits for delay minimization, when logic replication is not allowed ({\sc CN}). The problem of delay minimization when logic replication is allowed ({\sc CA}) has been well studied, and is known to be solvable in polynomial-time \cite{Wong1}. However, unbounded logic replication can be quite expensive. Thus, {\sc CN} is an important problem. We show that selected variants of {\sc CN} are {\bf NP-hard}. We also obtain approximability and inapproximability results for these problems. A preliminary version of this paper appeared in \cite{Don15}.
Max-Margin based Discriminative Feature Learning
Venue: arXiv cs.LG 2017
Year: 2017

In this paper, we propose a new max-margin based discriminative feature learning method. Specifically, we aim at learning a low-dimensional feature representation, so as to maximize the global margin of the data and make the samples from the same class as close as possible. In order to enhance the robustness to noise, a $l_{2,1}$ norm constraint is introduced to make the transformation matrix in group sparsity. In addition, for multi-class classification tasks, we further intend to learn and leverage the correlation relationships among multiple class tasks for assisting in learning discriminative features. The experimental results demonstrate the power of the proposed method against the related state-of-the-art methods.
Quasi-perfect Lee Codes of Radius 2 and Arbitrarily Large Dimension
Venue: arXiv cs.IT 2017
Year: 2017

A construction of 2-quasi-perfect Lee codes is given over the space $\mathbb Z_p^n$ for $p$ prime, $p\equiv \pm 5\pmod{12}$ and $n=2[\frac{p}{4}]$. It is known that there are infinitely many such primes. Golomb and Welch conjectured that perfect codes for the Lee-metric do not exist for dimension $n\geq 3$ and radius $r\geq 2$. This conjecture was proved to be true for large radii as well as for low dimensions. The codes found are very close to be perfect, which exhibits the hardness of the conjecture. A series of computations show that related graphs are Ramanujan, which could provide further connections between Coding and Graph Theories.
Kalman Filtering over Fading Channels: Zero-One Laws and Almost Sure Stabilities
Venue: arXiv cs.SY 2017
Year: 2017

In this paper, we investigate probabilistic stability of Kalman filtering over fading channels modeled by $\ast$-mixing random processes, where channel fading is allowed to generate non-stationary packet dropouts with temporal and/or spatial correlations. Upper/lower almost sure (a.s.) stabilities and absolutely upper/lower a.s. stabilities are defined for characterizing the sample-path behaviors of the Kalman filtering. We prove that both upper and lower a.s. stabilities follow a zero-one law, i.e., these stabilities must happen with a probability either zero or one, and when the filtering system is one-step observable, the absolutely upper and lower a.s. stabilities can also be interpreted using a zero-one law. We establish general stability conditions for (absolutely) upper and lower a.s. stabilities. In particular, with one-step observability, we show the equivalence between absolutely a.s. stabilities and a.s. ones, and necessary and sufficient conditions in terms of packet arrival rate are derived; for the so-called non-degenerate systems, we also manage to give a necessary and sufficient condition for upper a.s. stability.
Minimum Probabilistic Finite State Learning Problem on Finite Data Sets: Complexity, Solution and Approximations
Venue: arXiv cs.FL 2017
Year: 2017

In this paper, we study the problem of determining a minimum state probabilistic finite state machine capable of generating statistically identical symbol sequences to samples provided. This problem is qualitatively similar to the classical Hidden Markov Model problem and has been studied from a practical point of view in several works beginning with the work presented in: Shalizi, C.R., Shalizi, K.L., Crutchfield, J.P. (2002) \textit{An algorithm for pattern discovery in time series.} Technical Report 02-10-060, Santa Fe Institute. arxiv.org/abs/cs.LG/0210025. We show that the underlying problem is $\mathrm{NP}$-hard and thus all existing polynomial time algorithms must be approximations on finite data sets. Using our $\mathrm{NP}$-hardness proof, we show how to construct a provably correct algorithm for constructing a minimum state probabilistic finite state machine given data and empirically study its running time.
Profinite Techniques for Probabilistic Automata and the Markov Monoid Algorithm
Venue: arXiv cs.FL 2017
Year: 2017

We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it; it has been recently shown that the Markov Monoid algorithm, based on algebra, is the most correct algorithm so far. The first contribution of this paper is to give a characterisation of the Markov Monoid algorithm. The second contribution is to develop a profinite theory for probabilistic automata, called the prostochastic theory. This new framework gives a topological account of the value 1 problem, which in this context is cast as an emptiness problem. The above characterisation is reformulated using the prostochastic theory, allowing us to give a simple and modular proof.
Optimizing production scheduling of steel plate hot rolling for economic load dispatch under time-of-use electricity pricing
Venue: arXiv cs.SY 2017
Year: 2017

Time-of-Use (TOU) electricity pricing provides an opportunity for industrial users to cut electricity costs. Although many methods for Economic Load Dispatch (ELD) under TOU pricing in continuous industrial processing have been proposed, there are still difficulties in batch-type processing since power load units are not directly adjustable and nonlinearly depend on production planning and scheduling. In this paper, for hot rolling, a typical batch-type and energy intensive process in steel industry, a production scheduling optimization model for ELD is proposed under TOU pricing, in which the objective is to minimize electricity costs while considering penalties caused by jumps between adjacent slabs. A NSGA-II based multi-objective production scheduling algorithm is developed to obtain Pareto-optimal solutions, and then TOPSIS based multi-criteria decision-making is performed to recommend an optimal solution to facilitate filed operation. Experimental results and analyses show that the proposed method cuts electricity costs in production, especially in case of allowance for penalty score increase in a certain range. Further analyses show that the proposed method has effect on peak load regulation of power grid.
On the Geometric Ergodicity of Metropolis-Hastings Algorithms for Lattice Gaussian Sampling
Venue: arXiv cs.IT 2017
Year: 2017

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm from Markov chain Monte Carlo (MCMC) methods is adapted for lattice Gaussian sampling. Two MH-based algorithms are proposed, which overcome the restriction suffered by the default Klein's algorithm. The first one, referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm, tries to establish a Markov chain through an independent proposal distribution. We show that the Markov chain arising from the independent MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast regardless of the initial state. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, leading to a predictable mixing time. In order to further exploit the convergence potential, a symmetric Metropolis-Klein (SMK) algorithm is proposed. It is proven that the Markov chain induced by the SMK algorithm is geometrically ergodic, where a reasonable selection of the initial state is capable to enhance the convergence performance.
Code generator matrices as RNG conditioners
Venue: arXiv cs.IT 2017
Year: 2017

We quantify precisely the distribution of the output of a binary random number generator (RNG) after conditioning with a binary linear code generator matrix by showing the connection between the Walsh spectrum of the resulting random variable and the weight distribution of the code. Previously known bounds on the performance of linear binary codes as entropy extractors can be derived by considering generator matrices as a selector of a subset of that spectrum. We also extend this framework to the case of non-binary codes.
Matched Multiuser Gaussian Source-Channel Communications via Uncoded Schemes
Venue: arXiv cs.IT 2017
Year: 2017

We investigate whether uncoded schemes are optimal for Gaussian sources on multiuser Gaussian channels. Particularly, we consider two problems: the first is to send correlated Gaussian sources on a Gaussian broadcast channel where each receiver is interested in reconstructing only one source component (or one specific linear function of the sources) under the mean squared error distortion measure; the second is to send correlated Gaussian sources on a Gaussian multiple-access channel, where each transmitter observes a noisy combination of the source, and the receiver wishes to reconstruct the individual source components (or individual linear functions) under the mean squared error distortion measure. It is shown that when the channel parameters match certain general conditions, the induced distortion tuples are on the boundary of the achievable distortion region, and thus optimal. Instead of following the conventional approach of attempting to characterize the achievable distortion region, we ask the question whether and how a match can be effectively determined. This decision problem formulation helps to circumvent the difficult optimization problem often embedded in region characterization problems, and it also leads us to focus on the critical conditions in the outer bounds that make the inequalities become equalities, which effectively decouple the overall problem into several simpler sub-problems. Optimality results previously unknown in the literature are obtained using this novel approach. As a byproduct of the investigation, novel outer bounds are derived for these two problems.
The Pareto Frontier for Random Mechanisms
Venue: arXiv cs.GT 2017
Year: 2017

We study the trade-offs between strategyproofness and other desiderata, such as efficiency or fairness, that often arise in the design of random ordinal mechanisms. We use approximate strategyproofness to define manipulability, a measure to quantify the incentive properties of non-strategyproof mechanisms, and we introduce the deficit, a measure to quantify the performance of mechanisms with respect to another desideratum. When this desideratum is incompatible with strategyproofness, mechanisms that trade off manipulability and deficit optimally form the Pareto frontier. Our main contribution is a structural characterization of this Pareto frontier, and we present algorithms that exploit this structure to compute it. To illustrate its shape, we apply our results for two different desiderata, namely Plurality and Veto scoring, in settings with 3 alternatives and up to 18 agents.